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Left-handed behavior of combined and fishnet structures

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Leea

Quantum Photonic Science Research Center and BK21 Program Division of Advanced Research

and Education in Physics, Hanyang University, Seoul 133-791, Republic of Korea

Received 9 November 2007; accepted 9 December 2007; published online 13 February 2008

The left-handed LH behavior of a combined structure of cut wire pair and continuous wire was

experimentally studied. It was found that the LH behavior of a combined structure can still be

observed as the width of cut wire pair increases until the cut wire joins the continuous wire, theso-called fishnet structure. These structures were designed, fabricated, and measured in the

microwave frequency regime. In addition, we report the experimental results of the parametric study

on the fishnet structure, which are also compared with the previous theoretical studies. © 2008

American Institute of Physics. DOI: 10.1063/1.2841726

I. INTRODUCTION

Since the first experimental evidence for the left-handed

material LHM by Smith et al.,1

a large number of experi-

mental verifications for the existence of LHM in the micro-

wave and the optical regimes have been reported by many

researchers.2–6 In general, LHM is an artificial material and

consists of “magnetic component,” providing a negative

magnetic permeability 0, and “electric component,”

yielding a negative electric permittivity 0. It is well

known that it is not difficult to obtain a medium with 0,

e.g., by a periodic array of wires, at frequencies smaller than

the plasma frequency. The medium with 0 is, however,

still a major challenge for researchers since it occurs only in

a narrow frequency band. To date, besides the early invented

split-ring resonator SRR structure, there are several differ-

ent structures for achieving a negative magnetic permeabil-

ity, such as S-shaped,7-shaped,

8and -shaped structures.

9

To obtain the negative magnetic permeability for these struc-tures, the magnetic field vector H must be perpendicular to

the sample plane. This means that the incident electromag-

netic microwave has to propagate parallel to the sample

plane. Hence, a larger number of layers are required to fully

cover the incident beam, which is a major drawback for the

fabrication of LHMs working at terahertz and optical fre-

quencies, considering the current nanofabrication technol-

ogy. Therefore, an alternative to the SRR design is necessary

to overcome the aforementioned difficulties. Shalaev et al.4

have shown that the cut wire pair can replace the SRR for the

magnetic resonance. The cut wire pair consists of a pair of

finite-length wires separated by a dielectric layer. This struc-

ture exhibits not only a magnetic resonance but also an elec-tric resonance as in the SRR. Theoretically, it might be pos-

sible to obtain the LHM using only an array of cut wire pairs.

However, the recent experiments have revealed that an effi-

cient approach to achieve the LH behavior by employing the

cut wire pairs is to combine them with continuous wires.10–12

Several different designs, utilizing this idea for the LHM,

have been reported. Zhou et al.13

investigated the LHM

based on the H-shaped wires, which exhibits a negative re-

fraction index in the microwave range. Dolling et al.6,14

in-

troduced a modification with rectangular structures the so-

called fishnet structure and demonstrated the LH

characteristics at a wavelength of 780 nm, while Zhang et

al.3

employed an array of elliptical apertures, showing the

LH behavior in the near-infrared regime. Recently, Kafesaki

et al.15

have provided in detail the theoretical parametric

study on the fishnet structure and shown the origin of supe-

rior performance of the fishnet structure. They introduced a

simple LC model to describe the fishnet structure.

In this paper, we investigated experimentally the LH be-

havior of the combined structure of cut wire pair and con-

tinuous wire. In addition, we report the experimental results

of the parametric study of the fishnet structure. The results

were also compared with the previous theoretical studies.15,16

II. EXPERIMENT

The combined and the fishnet structures were fabricated

using the conventional printed circuit board PCB process

with copper patterns 36 m thick on both sides of a dielec-

tric PCB 0.4 mm thick with a dielectric constant of 4.8.

The periodicity along the x and the y directions was achieved

by printing a two-dimensional array of patterns on the planar

PCB. The periodicity along the z direction was obtained by

stacking a number of identical pattern boards with a lattice

constant of a z = 1.0 mm. For the combined structure, the geo-

metrical parameters are defined in Fig. 1a, similar to Refs.

10 and 11. The length of cut wire pair is l =5.5 mm, the

widths of cut wire and continuous wire are wcut wire = wwire

=1.0 mm. The unit-cell dimensions in the x and the y direc-tions of the combined structure array are a x =3.5 mm and

a y =7.0 mm. For the fishnet structure, the geometrical param-

eters are depicted in Fig. 1b, where the slab length is kept

constant to be lslab =5.5 mm. The combined and the fishnet

structures were designed, built, and measured in the micro-

wave range. We performed the transmission measurements in

free space, using a Hewlett-Packard E8362B network ana-

lyzer connected to the microwave standard-gain horn anten-

nas. In this measurement, the electromagnetic wave was in-

cident normal to the patterned PCB.

aAuthor to whom correspondence should be addressed. Electronic mail:

[email protected].

JOURNAL OF APPLIED PHYSICS 103, 033107 2008

0021-8979/2008/1033 /033107/4/$23.00 © 2008 American Institute of Physics103, 033107-1

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http://dx.doi.org/10.1063/1.2841726

http://dx.doi.org/10.1063/1.2841726

http://dx.doi.org/10.1063/1.2841726

http://dx.doi.org/10.1063/1.2841726

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III. RESULTS AND DISCUSSION

Figure 2 shows the measured transmission spectra of the

cut wire pair structures with different numbers of layers,

where the width of cut wire is 1.0 mm. Clearly, there is a

band gap between 13.4 and 14.8 GHz in the transmission

spectra. This band gap becomes more evident when the num-

ber of layers increases, as expected. Another band gap begins

to be formed at 17 GHz. The observed results are similarto those of Refs. 10 and 11. Hence, it is confirmed that the

first band gap in 13.4–14.8 GHz is due to the magnetic reso-

nance, providing a negative magnetic permeability, and the

second band gap starting at 17 GHz is due to the electric

resonance, providing a negative electric permittivity. This re-

sult reveals that the cut wire pair structure exhibits both a

magnetic and an electric resonance as a SRR. However, the

resonance frequencies are different and very difficult to over-

lap them, as it was shown in Ref. 16. Combining the cut wire

pairs with continuous wires, one can get a combined struc-

ture that exhibits the LH behavior.

Figure 3 presents the measured transmission spectra of

the cut wire pair, the continuous wire, and the combined

structures, respectively. For this measurement, all structures

here consist of three layers. The dotted line gives the trans-

mission spectrum of the continuous wire structure, while the

dashed and solid lines show the transmission spectra of the

cut wire pair and the combined structures, respectively. As

shown in Fig. 3, we could not observe a plasma cutoff fre-

quency of the continuous wire structure, which might be

higher than the measured frequency range. The cut wire pairstructure displays a stop band between 13.4 and 14.8 GHz,

corresponding to the magnetic resonance frequency range

where 0, while the combined structure exhibits a pass

band; this pass band exactly coincides with the stop band of

the cut wire pair structure. Based on these results and the

previous studies,10–12

it is confirmed that the pass band be-

tween 13.4 and 14.8 GHz in the transmission spectrum of the

combined structure provides a clear evidence for the appear-

ance of the LH behavior. There exists another pass band in

15.3–17.3 GHz. It is known that the cut wire pair also ex-

hibits the electric resonance. Thus, when the cut wire pair is

combined with the continuous wire, the plasma frequency of

a combined structure is much lower than that of continuouswire alone.

11,17Therefore, to explain the pass band between

15.3 and 17.3 GHz, besides permeability, permittivity should

also be positive. Thus, this is a right-handed transmission

band.

Figure 4 presents the measured transmission spectra of

the cut wire pair and the combined and the fishnet structures.

The dotted line gives the transmission spectrum of the com-

bined structure, while the dashed line shows the transmission

spectrum of the fishnet structure. Note that in this case the

slab length lslab and the wire width wwire of the fishnet struc-

ture are 5.5 and 1.0 mm, respectively. As can be seen in Fig.

4, there also exist two pass bands in the transmission spectra

FIG. 1. Color online The unit cell of a combined structure and b fishnet

structure. c and d are the photographs of one side of fabricated combined

and fishnet structures, respectively.

FIG. 2. Color online Measured transmission spectra of the cut wire pair

structure with different numbers of layers in the propagation direction.

FIG. 3. Color online Measured transmission spectra of the cut wire pair,

the continuous wire, and the combined structures.

033107-2 Lam et al. J. Appl. Phys. 103, 033107 2008


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of the fishnet structure similar to the case of the combined

structure. Two pass bands are separated by a shallow dip, inwhich the first pass band between 15.5 and 16.2 GHz exhib-

its the LH behavior, while the second one starting at

17.3 GHz is the right-handed transmission.15

Furthermore,

the LH peak of the fishnet structure is shifted to high fre-

quency compared to that of the combined structure. This

result is in good agreement with the previous theoretical

study and is explained by the simple LC model proposed by

Kafesaki et al. The LC model describing the fishnet structure

is similar to that of the cut wire pair structure, with an addi-

tional inductance of the connected wire between neighboring

slabs. It leads to the magnetic resonance of the fishnet struc-

ture higher than that of the cut wire pair structure and is

expressed by fishnet2 = cut wire pair

2 + connected wire2 . Therefore,

the upward shift of the LH peak in the fishnet structure is due

to the inductance of the connected wire. Thus, the fishnet

structure can be considered as a combination of the cut wire

pairs with continuous wires which is physically connected.

We can imagine that when the width of cut wire pair in-

creases until the cut wire merges with the adjacent continu-

ous wire, the combined structure will become the fishnet

structure.

Figure 5 shows the measured transmission spectra of

various fishnet structures, in which the length of the slab is

kept to be constant of 5.5 mm, while the width of the wire

was varied from 1.0 to 3.0 mm. As can be seen, the peak that

exhibits the LH behavior is shifted to high frequency as in-

creasing the width of the wire. In case the width of the wire

is 3.0 mm, we cannot see the LH peak because it is higher

than the measured frequency range. This result shows that

the LH peak of the fishnet structure strongly depends on the

width of the wire. The observed results can be explained

based on the LC model.15

In this model, the magnetic reso-

nance frequency of the fishnet structure is given by

f m = m

2 1

lslab2

+wwire

lslablwirewslab

. 1

Here, lslab is the length of the slab and lwire is the distance

between slabs connected wire. wslab and wwire are the

widths of the slab and the wire, respectively see Fig. 1b.Equation 1 yields that the magnetic resonance frequency of

the fishnet structure is proportional to the square root of

width of the wire. This model agrees with the experiment, as

shown in Fig. 5. Another interesting feature in Fig. 5 is that

the transmission gradually decreases as the width of the wire

becomes larger and tends to disappear when wwire = wslab.

This effect was also studied by the previous theoretical study

in the infrared frequency.4

This result suggests that the rela-

tive ratio between the width of the slab and the wire plays an

important role to obtain the LH behavior with high transmis-

sion. In the extreme case where the width of the wire de-

creases until wwire =0, the fishnet structure turns into the cut

wire pair structure. This structure is like a magnetic compo-nent, providing the negative permeability. The measured

transmission spectra of the cut wire pair structure were

shown in Fig. 2. Theoretically, it might be possible to obtain

the LH behavior using only an array of cut wire pairs. How-

ever, the recent experiments have revealed that an efficient

approach to achieve the LH behavior by employing the cut

wire pairs is to combine them with continuous wires, as

shown in Fig. 3.

Another interesting result is presented in Fig. 6. We plot

here the measured transmission spectra of several different

fishnet structures. In this study, the slab length and the wire

width are lslab =5.5 mm and wwire =1.0 mm, respectively. The

unit-cell dimension in the y direction is kept constant to be7.0 mm, while it is varied from 3.5 to 6.5 mm in the x direc-

tion. It means that the slab width wslab was changed. As can

be seen in Fig. 6, the LH peak is shifted to low frequency

when increasing the distance between wires. It is known that

for a given unit cell of the fishnet structure, the slab induc-

tance is considered as an inductance of parallel plates; thus,

it is inversely proportional to the width of the slab wslab

Lslab1 /wslab. It is similar to the inductance of the cut wire

pair in the combined structure. In other words, the slab in-

ductance depends on the distance between wires. Therefore,

when the distance between wires increases, the total induc-

tance of the fishnet structure will decrease. Hence, the ob-

FIG. 4. Color online Comparison of the measured transmission spectra

between combined and fishnet structures.

FIG. 5. Color online Measured transmission spectra of several fishnet

structures. The width of the slab is kept to be wslab =5.5 mm and the widths

of the wire are wwire =1.0, 2.0, and 3.0 mm.



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served downward LH peak shift in Fig. 6 is due to an in-

crease of the slab inductance. This result is good agreement

with Eq. 1.

Equation 1 also suggests that the magnetic resonance

frequency increases as the distance between slabs is reduced

reducing the connected wire between slabs. Indeed, this

feature was also verified by our experiments that measured

the dependence of the transmission spectra on the distance

between slabs, as clearly seen in Fig. 7. In this study, the

distance between wires is kept constant, 4.5 mm, while the

distance lwire between slabs is varied from 1.5 to 3.5 mm.

The solid line exhibits the transmission spectrum of the fish-

net structure with the distance of 1.5 mm between slabs,

while the dotted line gives the transmission spectrum withthe distance of 3.5 mm between slabs. As can be seen in Fig.

7, the LH peak is shifted from 14 to 16 GHz when the dis-

tance between slabs decreases from 3.5 to 1.5 mm. It means

that the LH peak is inversely proportional to the distance

between the neighboring slabs. The observed result can be

explained due to the change of current distribution in the

slabs and connected wire.15

As the separation of the neigh-

boring slabs increases, the magnetic resonance frequency de-

creases, and therefore the LH peak is shifted to lower fre-

quency, as shown in Fig. 7. This phenomenon is analogous to

that of the cut wire pairs alone and has been analyzed byZhou et al.

16

IV. CONCLUSI ONS

In this paper, we have investigated experimentally the

LH behavior of the combined structure of cut wire and con-

tinuous wire. We have also reported the experimental results

of the parametric study on the fishnet structure. Our results

show that the LH peak depends strongly on the geometric

parameters of the periodic structures. Especially, the relative

ratio between the slab length and the wire width seems to

play an important role in obtaining the LH behavior with a

high transmission. This result is in good agreement with theprevious theoretical studies. In addition, these results tell us

that the fishnet structure is a combined structure where the

cut wire merges with the adjacent continuous wire.

ACKNOWLEDGMENTS

This work was supported by MOST/KOSEF through the

Quantum Photonic Science Research Center, Seoul, Korea.

1D. Smith, W. Padilla, D. Vier, S. Nemat-Nesser, and S. Chultz, Phys. Rev.

Lett. 84, 4184 2000.2M. Gokkavas, K. Guven, I. Bulu, K. Aydin, R. S. Penciu, M. Kafesaki, C.

M. Soukoulis, and E. Ozbay, Phys. Rev. B 73, 193103 2006.3S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J.Brueck, Phys. Rev. Lett. 95, 137404 2005.

4V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P.

Drachev, and A. V. Kildishev, Opt. Lett. 30, 3356 2005.5S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M.

Osgood, Opt. Express 13, 4922 2005.6G. Dolling, W. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett. 32, 53

2007.7H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and

J. A. Kong, Phys. Rev. E 70, 057605 2004.8J. Huangfu, L. Ran, H. Chen, X. M. Zhang, K. Chen, T. M. Grzegorczyk,

and J. A. Kong, Appl. Phys. Lett. 84, 1537 2004.9Z. G. Dong, S. Y. Lei, Q. Li, M. X. Xu, H. Liu, T. Li, F. M. Wang, and S.

N. Zhu, Phys. Rev. B 75, 075117 2007.10

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, Phys. Rev.

B 73, 041101 2006.

11K. Guven, M. D. Caliskan, and E. Ozbay, Opt. Express 14, 8685 2006.12

A. O. Cakmak, K. Guven, and E. Ozbay, Phys. Status Solidi B 244, 1188

2007.13

J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, Appl.

Phys. Lett. 88, 221103 2006.14

G. Dolling, C. Enkrich, W. Wegener, C. M. Soukoulis, and S. Linden, Opt.

Lett. 31, 1800 2006.15

M. Kafesaki, I. Tsiapa, N. Katsaraki, Th. Koschny, C. M. Soukoulis, and

E. N. Economon, Phys. Rev. B 75, 235114 2007.16

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, Opt. Lett. 31,

3620 2006.17

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Phys.

Rev. Lett. 93, 107402 2004.

FIG. 6. Color online Measured transmission spectra vs frequency of dif-

ferent fishnet structures. The widths of the slab and the wire are 5.5 and

1.0 mm, respectively. The distance between slabs is 1.5 mm, while the

wire’s distance varies from 3.5 to 6.5 mm.

FIG. 7. Color online Measured transmission spectra of two different fish-

net structures. The widths of the slab and wire are 5.5 and 1.0 mm, respec-

tively. The distance between wires is kept at 4.5 mm but the distances lwire

between slabs are 1.5 and 3.5 mm.



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